Conditional Quantile Analysis for Functional Covariates

• Activity Number: 619
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kehui Chen*+ and Hans-Georg Mueller
• Companies: University of California, Davis and University of California, Davis
• Keywords: Functional Data Analysis ; Quantile Analysis ; Growth Charts

Abstract

Motivated by the conditional growth charts problem, we develop a method for conditional quantile analysis when predictors take values in a functional space. The proposed method aims at estimating conditional distribution functions under a generalized functional regression framework. This approach facilitates the balancing of model flexibility and the curse of dimension for the infinite-dimensional functional predictors. Its good performance in comparison with other methods, both for sparsely and densely observed functional covariates, is demonstrated by theory as well as in simulations and an application to growth curves, where the proposed method can be used to assess the entire growth pattern of a child by relating it to the predicted quantiles of adult height.